Engineering Of The High Frequency Of Trigonometric Function Integral Calculation

In the engineering problems, there are many fields relating to the highly frequency trigonometric functions integral operation problems.This article will make researches on two fields:on the one hand, this paper makes research and computes the integrals of the magnetic and the electric fields of the middle half space’s line current source of the geological exploration; On the other hand, this paper makes research and computes the integrals of single-freedom second order oscillation system of the mechanical vibration theory.This paper is made up of four chapters:In the first chapter, this paper introduces the relating fields of layered half space’s line current source and second order oscillational system, then expounds the present situations of the research problems of this kind, finally shows the main works, the research methods and significances of this paper.In the second chapter, this essay puts forward a kind of high frequency trigonometric functions integral operation problems that occur at the magnetic and the electric fields of the middle half space’s line current source of the geological exploration whose forms are (?)f(t)sin(ωt)dt and (?)f(t)cos(ωt)dt, this paper will use the Epsilon algorithm and m-W transform which belong to extrapolation methods and Clenshaw-Curtis-self-adaption algorithm to compute them, at the same time, this chapter will show their results of numerical experiments when they are used in this kind of questions.In the third chapter, we mainly introduces the second order oscillation system, at the same time,we get the solution of the forced vibration of single-degree-of-freedom system that is Duhamel integral whose form is (?)f(τ)e-ξωn(t-τ)sin[ωd(t-τ)]dτ, then this paper uses the Epsilon algorithm and Clenshaw-Curtis-self-adaption algorithm to calculate the integrals, and shows the similarities and difference, advantages and disadvantages of the two methods.In the last chapter, it summarizes the object of this paper which is high frequency trigonometric functions integral operation problems and its research methods, then it points out the disadvantages and advantages of this method which is used in this paper, at last, it also points out the developments of high frequency trigonometric functions integral operation problems.